I would take the job.
Because I am confident that I am able to tackle it, and it's a useful experience.
Personally, I don't care about unit tests, and documentation.. I can generate a diagram from the database - it's MVC, isn't it?
Even if it's CakePHP. 1.3 is not too bad.
I would take it.
Because there are lots of projects like that out there in the real world.

If the deadline is in a couple of weeks and there is a team working on it already, I'd say: screw them.
I would take on a project like that if the deadline was a couple of months - depends on the existing team. But not in this situation.

If you want to take the job, ideally explaining to the managers that their target date is unrealistic, because there current codebase was developed by someone else that didn't follow best practices, you can't guarantee your work because you can not depend on someone else got it right.

I can draw parallels with people in the plumbing and electrical trade, that got into similar situations and walk away.